If the temperature is the same in both places, the Boyle's law can be defined as following:
p1V1 = p2V2
where p1 - initial pressure, V1 - initial volume, p2 - final pressure, V2 - final volume.
From here:
V2 = p1V1 / p2
As a result:
V2 = 1.00 atm × 315 ml / 0.775 atm = 406 ml
Answer: 406 ml
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